Smarter males were more able to get mates (perhaps through control of resources among other things)?

Smarter mates were, or were able to make themselves appear, more attractive?

To me it's fairly evident that sexual selection played a large role in brain development.

You are probably not wrong.

He is likely right, because genes for intelligence are very often on the X-chromosome:

https://www.psychologytoday.com/articles/201109/the-incredib...

Cool story, bro.